Page 170 - Petrophysics
P. 170
PERMEABILITY-POROSITY RELATIONSHIPS 143
Combining Equations 3.70 and 3.75 yields:
(3.77)
and the tortuosity is:
Using the same approach, the effects of flow path on the permeability
can be evaluated. Applying Poiseiulle’s equation to the ith tube, the flow
rate in the ith tube, qi, is equal to:
(3.79)
where rpai, 1, and AP are, respectively, the apparent radius of the
ith tube, fluid viscosity, and pressure differential across the unit block.
For n tubes, the total flow rate q is:
(3.80)
and, assuming A2 is constant, the flow rate is:
(3.81)
Applying Darcy’s law to the unit block, the flow rate is equal to:
(3.82)
Combining Equations 3.76, 3.77, 3.79, 3.80, and 3.81, and solving for
the apparent permeability of the block, ka:
(3.83)